Social anxiety is a common condition and there are many ways to deal with its symptoms. As per my experience, getting a dog can help you a lot. Please tell me guys which is the best breed of dog for emotional support?
There's nothing inherantly wrong with all the pitties and chihuahua/terrier mixes at the shelter. They get euthanized because nobody wants them, but both breeds are intelligent, loving, and trainable. People are always asking me what breed Laurel is. There's nothing special about her at all, she's just a puppy mill overstock who got the love and training that all dogs deserve.
Generally it's not the breed, but the personality. Keep in mind, that in true theraputic service dog situations, the dog will be required to be washed and groomed for visiting clients. Which may require daily attention. In terms of breed, it helps to find a breeder who is specializing in temperament (as well as health). Size (for convenience and mobility) is a consideration. Minimal breed faults (hip dysplasia) or breathing issues if working in extreme temperature conditions. Have an instinctual "nurturing" capacity. (Some would call it "loving") but is simply attention, loyalty, companionship, sensitivity, awareness. Consider the kind of breeds which seem to exemplify these traits (as in what kinds of jobs do you already see the breed doing). Then there are "lap dog" breeds (actually bred) to be companion dogs, you'd want one with a high level of intelligence and capacity for training (or at least acclimation to the situation required). Breeds that are generally confident, consistent, non agressive, socialable, compatible. Comfortable in limited areas (for apartment living) as opposed to requiring large areas for exercise.
One specific "breed" can't be selected for you without knowing your specifics.
Almost any breed of dog could potentially work out, but you should decide if you want an active dog that needs to run, a medium energy dog that can get buy on a short walk, or a couch potato that you'd have to carry around the block. Given your anxiety, it might be advisable to get a medium energy dog which will force you to get out for fresh air in case your anxiety is cooping you up indoors. Also, having a dog and walking it in your neighborhood is the single best way to chit chat with other people or dog owners.
If you're active, I would recommend a Labrador retriever, Golden Retreiver (my first choice for high energy) , or German Shepherd (German not American bred). For a medium energy, a Boston Terrier, Cocker Spaniel, Cavalier King Charles (though can have many health issues), Collie, etc, for low energy Chihuahua, Mastiff, Greyhound, French Bulldog (more health issues), Shih Tzu, Havanese, Maltese, etc.
As other have pointed out, the temperament is the most important thing in any of the breeds. There are some really nice mixed breeds at dog shelters and most mixed breeds are cheaper to buy, and will generally have less health issues that pure bred dogs (due to pedigree breeding standards).
I have anxiety myself and got a Boston Terrier two months ago and he's awesome. He's low-medium energy and forces me to get out and mingle, take him to the beach, hikes, etc. He's a puppy so he really gets a lot of attention, people love talking about their dogs.
I wanted a Golden Retriever but I don't want to exercise it in the winter outside everyday for an hour or more. The Boston Terrier will be ok with a brisk walk in the winter as they don't like the cold. A dog like a chihuahua can get by walking from the kitchen to the living room a few times a day.
God luck, and congratulations on your decision to get a dog!